### Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

### Stonehenge

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

### Maximum Flow

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

# Beam Me Up

##### Stage: 5 Challenge Level:

Understanding the formula $\psi = \int \kappa ds$

Consider a beam which is a perfect arc of a circle

Calculate $\int \kappa ds$ along this section. Can you relate $\phi$ to $\psi$?

Finding $v$ in terms of $\kappa$ and $x$

Consider a very small section of the beam, curved length $\delta s$ and vertical deflection $- \delta v$. Can you express $\delta v$ in terms of the other quantities?